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On the metamathematics of impredicative set theory

100%

Marek W.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction....................................................................................... 5 0. Set theory M.................................................................................. 6 1. Reflection principles in M.......................................................... 12 2. The trees....................................................................................... 18 3. Ordinal trees. Constructibility in M........................................... 25 4. Minimal model for M................................................................... 30 5. Forcing in M, independence results for M.............................. 34 6. Hierarchy of formulas in M......................................................... 37 References....................................................................................... 41

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Some properties of stationary sets

65%

Di Prisco C. A., Marek W.

Instytut Matematyczny Polskiej Akademii Nauk

XX

CONTENTS Introduction..................................................................5 1. Derivative of a stationary set...................................7 2. Stationary degrees ...............................................13 3. Subsets of $P_ϰ(λ)$..............................................19 4. Stationary subsets of $P_ϰ(λ)$.............................25 5. Superstationary substes of $P_ϰ(λ)$....................32 6. End-stationary subsets of $P_ϰ(λ)$......................34 References................................................................37

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Spectrum of L

65%

Marek W., Rasmussen K.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 0. Motivation, results to be used in the sequel ................5 1. Slicing $L_α$'s ..........................................................10 2. Hereditarily countable, definable elements ................13 3. Spectrum of L.............................................................15 4. The width of elements of spectrum ............................19 5. Non-uniform strong definability ..................................26 6. Solution to a problem of Wilmers................................32 7. Supremum of spectrum of L........................................36 References.....................................................................38

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Stable sets, a characterization of $β_2$-models of full second order arithmetic and some related facts

48%

Marek W.

Fundamenta Mathematicae

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1974-1975

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tom 82

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nr 2

175-189

5

On the number of models of the Kelley-Morse theory of classes

37%

Marek W., Zbierski P.

Fundamenta Mathematicae

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1980

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tom 109

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nr 3

169-173

6

Some comments on the paper by Artigue, Isambert, Perrin and Zalc

36%

Marek W.

Fundamenta Mathematicae

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1978

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tom 101

|

nr 3

227-228

7

ω-models of second order arithmetic and admissible sets

31%

Marek W.

Fundamenta Mathematicae

|

1978

|

tom 98

|

nr 2

103-120

Ograniczanie wyników

4 Fundamenta Mathematicae

7 Marek W.

1 Di Prisco C. A.

1 Rasmussen K.

1 Zbierski P.

2 1983

1 1980

2 1978

1 1974

1 1973

On the metamathematics of impredicative set theory

Some properties of stationary sets

Spectrum of L

Stable sets, a characterization of $β_2$-models of full second order arithmetic and some related facts

On the number of models of the Kelley-Morse theory of classes

Some comments on the paper by Artigue, Isambert, Perrin and Zalc

ω-models of second order arithmetic and admissible sets